Is a dystopian surveillance state computationally possible?
You don't necessarily have to analyse it all. Just by having such data available you can achieve a lot in terms of surveillance, as long as you can retrieve relevant parts.

A few years ago there was a Radiolab podcast, "The Eye in the Sky" (there's a full transcript on the site). The basic idea is that you have a plane circling a city 24/7, and filming what goes on. If there was a crime somewhere, you retrieve the recordings after the event, and you can track back to where vehicles involved in the crime were coming from, and where they went after the crime. If nothing happens, you simply archive the data, and perhaps remove it after a month or so.

This method was used to solve a hit-and-run assassination of a police woman who was on her way to work. The gang who committed the attack were rather surprised when the police showed up at their secret hide-out a few days later, as they could see on the images where the cars involved went to later. At the time and place of the murder there were obviously no witnesses who could have done that. And this involved no computational processing at all.

The possibilities this opens up are just scary, as you can track pretty much anybody's movements without actually needing someone to follow them. Add to that street-level CCTV, and not much can happen without you being able to find out.

In this scenario there is no processing at all, but you could imaging simple processing steps, such as tracking vehicles or changes in the environment, which could be used to give clues about potentially 'interesting' events. So instead of using it 'passively' as a kind of memory, you could use that data to identify things that happened that you weren't aware of.

And this is without even any clandestine access to people's data. If you add that dimension, then you might even be able to identify crimes/etc before they even happen. Text processing can be quite fast, but is not easy to do, as presumably few people would openly communicate about things they were planning. So I guess we're still a long way away from that.

Of course there is the ethical dimension (which is mentioned in the podcast): who has access to that data, and who decides what it is used for? If you do, and you suspect your partner of being unfaithful, who/what would stop you from checking out their movements? Or check up on that politician who might have a secret affair, or a gambling issue, or who keeps being in the same locations as a well-known drug dealer. All rather scary.

While a complete analysis of all such data would be very heavy computationally, and fraught with false positives and recall problems, it might simply be enough to index it by time, location, and perhaps people involved (face recognition seems to be reasonably good, though still with a rather high error rate). This is enough already to make me feel worried about the future.